George Boole : Selected Manuscripts on Logic and its Philosophy

George Boole (1815-1864) is well known to mathematicians for his research and textbooks on the calculus, but his name has spread world-wide for his innovations in symbolic logic and the development and applications made since his day. The utility of "Boolean algebra" in computing has greatly increased curiosity in the nature and extent of his achievements. His work is most accessible in his two books on logic, "A mathematical analysis of logic" (1947) and "An investigation of the laws of thought" (1954). But at various times he wrote manuscript essays, especially after the publication of the second book; several were intended for a non-technical work, "The Philosophy of logic", which he was not able to complete. This volume contains an edited selection which not only relates them to Boole's publications and the historical context of his time, but also describes their strange history of family, followers and scholars have treid to confect an edition. The book will appeal to logicians, mathematicians and philosophers, and those interested in the histories of the corresponding subjects; and also students of the early Victorian Britain in which they were written.

A The Nature of Logic and the Philosophy of Mathematics.- I The Nature of Logic.- Logic is the science of reasoning.- Of what does reasoning consist?.- General Considerations.- Of our Conception of Things.- On the relations of individuals and classes.- Of the mode in which the mind combines.- and modifies its own conceptions.- Of the nature of Propositions.- Of the limitation of the subject of discourse.- Laws of the Mental Operation.- Comparison of the laws of elective symbols.- with the laws of arithmetical symbols.- Consequences of the above analogies.- Examples for Practice.- Of the interpretation of 0 and 1 as elective symbols.- Expression of the class not-men etc.- II Elementary Treatise on Logic not mathematical including philosophy of mathematical reasoning.- Of Signs.- Of Propositions.- Of the Quantity of Terms.- Of the Quality of Terms.- Division.- Of Some of the Varieties of Propositions.- Of the Limitation of Propositions.- Of the Conversion of Propositions.- Of Syllogism.- Conditions and Rules of Syllogistic Inference.- General Remarks on Primary Propositions.- Of Secondary Propositions.- Of the Demonstrations of Geometry.- Of the Foundations of Algebra.- Of the Differential Calculus.- The real nature of mathematical analysis.- III [Extracts from a notebook].- Miscellaneous Observations on Logic.- Of Inverse Operations.- Of signs.- B The Philosophical Interpretation of a Theory of Logic.- IV Prolegomena.- Results of the Analysis of Conception.- V On the Foundations of the Mathematical Theory of Logic and on the Philosophical Interpretation of Its Methods and Processes.- Analysis of the Operations of Conception as Exercised within the Sphere of Formal Logic.- Operations founded on Extension.- Operations founded on Intension.- Laws of Conception.- Addition.- Subtraction.- Composition.- Abstraction.- Law of mixed operations of Addition and Composition.- Analysis of Judgment as Exercised within the Sphere of Formal Logic.- Analysis of Reasoning as Exercised within the Sphere of Formal Logic.- On Systems of Notation.- Symbolical expression of the formal laws of Logic.- Analysis of Reasoning resumed.- VI [Preparatory Notes].- Of the nature and scope of Logic as considered a Science.- Definitions of Conception, Judgment and Reasoning.- [Conception].- Judgment.- Reasoning.- [Further Considerations].- VII General Summary.- Theory of Formal Logic.- C “The Philosophy of Logic” - A Sequel to “The Laws of Thought”.- VIII [Preface].- IX Table of Contents.- I: Of the ordinary Logic.- II: Of the operations of thought in relation to the science of number.- III: Of the Laws of Thought in Logic.- IV: Interpretation of Methods.- The Philosophy of Reasoning.- XI Logic.- Nature and Office of Signs.- Methods in Logic.- The Aristotelian Logic.- Sir W. Hamilton’s Theory of Syllogism.- The Theory of Professor De Morgan.- Of the Ultimate Laws of Thought.- Of the Method of This Work.- The Method of Algebra.- Method of This Work.- Results of This Method.- D Miscellaneous Matters, Letters and Fragments.- XII On Belief in Its Relation to the Understanding.- XIII The Philosophical Idea of Freedom.- Infinite evolution.- XIV Note [to Aristotle].- XV Philosophy of Mathematics.- II: On Geometry.- XVI [Various fragments, apparently late].- [Fragment 1].- [Fragment 2].- Digression on the Nature of Algebra.- [Fragment 3].- Principles of Expression.- Laws of the Symbols.- [Fragment 4].- [Fragment 5].- [Fragment 6].- [Fragment 7].- XVII Letters to Cayley, Lubbock and Penrose.- Arthur Cayley.- Cayley to Boole, 2 December 1847.- Boole to Cayley, 6 December 1847.- Cayley to Boole, 7 December 1847.- Boole to Cayley, 8 December 1847.- Boole to Cayley, 10 December 1847.- Cayley to Boole, 11 December 1847.- Boole to Cayley, 14 December 1847.- John William Lubbock.- Boole to Lubbock, 16 February 1849.- Boole to Lubbock, 22 February 1849.- John Penrose.- Boole to Penrose, 13 March 1855.- Textual Notes.- Explanation of the description of the material.- The two Signature systems “MM” and “RS”.- The Boole/Falk List of 1896.- Details on individual documents.- Notes on the individual chapters.- I: The Nature of Logic.- II: Elementary Treatise on Logic.- III: [Extracts from a notebook].- IV: Prolegomena.- V: On the Foundations of Logic.- VI: [Preparatory Notes].- VII: General Summary.- VIII: [Preface].- IX: Table of Contents.- X: The Philosophy of Reasoning.- XI: Logic.- XII: On Belief in Its Relation to the Understanding.- XIII: The Philosophical Idea of Freedom.- XIV: Note [to Aristotle].- XV: Philosophy of Mathematics.- XVI: [Various fragments, apparently late].- XVII: Letters to Cayley, Lubbock and Penrose.- Index of Names.- Index of Subjects.